Geodesic
On Generalized Bishop Frame of Null Cartan Curve in Minkowski 3-Space
Kragujevac Journal of Mathematics, Tome 43 (2019) no. 4, p. 559 .

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In this paper, we define generalized Bishop frame of a null Cartan curve in Minkowski $3$-space by using its Bishop's frame vector fields. We obtain the Cartan equations according to the generalized Bishop frame and give the relations between the generalized Bishop curvatures and Bishop curvatures. We show that among all null Cartan curves in $\mathbb{E}^{3}_{1}$, only the null Cartan cubic has two generalized Bishop frames, one of which coincides with its Bishop frame. We also show that there exists a null Cartan curve whose generalized Bishop curvatures and Bishop curvatures are equal, but whose generalized Bishop frame and Bishop frame do not coincide. As an application, we characterize a $k$-type null Cartan slant helices for $k\in\{0,1,2\}$ according to their generalized Bishop frame and give some examples.
Classification : 53C50 53A04, 53C40
Keywords: Bishop frame, Cartan frame, null Cartan curve, Minkowski space 
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     author = {Milica Grbovi\'c and Emilija Ne\v{s}ovi\'c},
     title = {On {Generalized} {Bishop} {Frame} of {Null} {Cartan} {Curve} in {Minkowski} {3-Space}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {559 },
     publisher = {mathdoc},
     volume = {43},
     number = {4},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2019_43_4_a4/}
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Milica Grbović; Emilija Nešović. On Generalized Bishop Frame of Null Cartan Curve in Minkowski 3-Space. Kragujevac Journal of Mathematics, Tome 43 (2019) no. 4, p. 559 . http://geodesic.mathdoc.fr/item/KJM_2019_43_4_a4/